1. Field of the Invention
The present invention relates to an exposure method for transferring a mask pattern onto a photosensitive substrate during photolithography processes in the manufacture of semiconductor devices, liquid crystal display devices, imaging devices (e.g. CCD), thin-film magnetic heads, etc. More particularly, the present invention relates to an exposure method which is suitably applied to a process in which exposure is sequentially carried out by the mix-and-match method with respect to two layers, that is, a layer called "middle layer", which requires no high resolution, such as an ion-implanted layer used in production of a semiconductor memory or the like, and a layer called "critical layer", which requires high resolution.
2. Related Background Art
Exposure apparatuses, e.g. step-and-repeat reduction projection type exposure apparatuses (steppers), are used in photolithography processes for producing semiconductor devices, liquid crystal display devices, etc. Generally, a semiconductor device such as a VLSI is formed by stacking a multiplicity of pattern layers on a wafer while effecting alignment for each layer. Among the pattern layers, a layer that needs the highest resolution is called "critical layer", and a layer that needs no high resolution, e.g. an ion-implanted layer used in production of a semiconductor memory or the like, is called "middle layer". In other words, the line width of a pattern which is exposed for the middle layer is wider than the line width of a pattern exposed for the critical layer.
There has been an increasing tendency for recent VLSI manufacturing factories to carry out exposure operations for different layers by using respective exposure apparatuses in a process for producing a single type of VLSI in order to increase the throughput (i.e. the number of wafers processed per unit time) in the production process. Under these circumstances, it has become common practice to carry out what is called "mix-and-match" exposure. In the mix-and-match exposure process, exposure for the critical layer is carried out by using a first stepper of high resolution which performs one-shot exposure with a demagnification ratio of 5:1, and exposure for the middle layer is carried out by using a second stepper of intermediate resolution which performs one-shot exposure with a demagnification ratio of 2.5:1. In this case, the size of the exposure field of the second stepper is twice as large as that of the first stepper in both lengthwise and breadthwise directions, and the throughput of the second stepper in the exposure process is approximately four times that of the first stepper. This will be explained below with reference to FIG. 35.
Assuming that, as shown in FIG. 35, exposure units on a wafer which are to be exposed by the first stepper are square shot areas SA.sub.11, SA.sub.12, SA.sub.13, SA.sub.14, . . . each surrounded by sides which are parallel to X- and Y-axes perpendicularly intersecting each other, an exposure area which is to be exposed by the second stepper is a shot area SB.sub.1 which is so large as to substantially contain the four shot areas SA.sub.11 to SA.sub.14. When exposure is to be carried out by the second stepper over the four shot areas SA.sub.11, SA.sub.12, SA.sub.13 and SA.sub.14 exposed by the first stepper, the second stepper effects alignment of the shot area SB.sub.1, which corresponds to the exposure field of the second stepper, on the basis of alignment marks (wafer marks) attached to the shot areas SA.sub.11 to SA.sub.14.
There is another conventional exposure method in which, for example, a step-and-scan type scanning exposure apparatus with a demagnification ratio of 4:1 is combined with either the above-described first or second stepper. The step-and-scan exposure is a process in which a shot area on a wafer which is to be exposed is stepped to a scanning start position, and thereafter a reticle, which serves as a mask, and the wafer are synchronously scanned with respect to a projection optical system, thereby sequentially transferring a pattern on the reticle onto the shot area. The exposure field of the scanning exposure apparatus is equal, for example, in the width of the non-scanning direction to the exposure field of the first stepper, but the exposure field width in the scanning direction of the scanning exposure apparatus is 1.5 times that of the first stepper. It should be noted that there are various combinations of different exposure field sizes of a plurality of exposure apparatuses used in the mix-and-match exposure method in addition to the above-described combinations.
Thus, the throughput of an exposure process can be increased by carrying out a mix-and-match exposure process using different exposure apparatuses in combination according to the resolution required for each layer on a wafer as described above. However, when exposure apparatuses having respective exposure fields of different sizes are used in combination, if a perpendicularity error remains in the array of shot areas (i.e. shot array) of the preceding layer, i.e. if the angle between the X- and Y-axes of the shot array deviates from 90.degree., a given overlay error arises. Such a perpendicularity error is due to the fact that the feed directions of the wafer stage driven by motors are not accurately perpendicular to each other.
For example, assuming that in FIG. 35 the imaginary straight line 23A passing through the centers of the shot areas SA.sub.13 and SA.sub.14 in the four shot areas of the preceding layer is parallel to the X-axis, if the angle between the X- and Y-axes of the shot array deviates from 90.degree. by an angle (perpendicularity error) W, the imaginary straight line 24 passing through the centers of the shot areas SA.sub.11 and SA.sub.13 tilts by the perpendicularity error W [rad] relative to the Y-axis. In this case, if exposure is carried out with the center of the subsequent shot area SB.sub.1 aligned with the center 25 of the four shot areas SA.sub.11, SA.sub.12, SA.sub.13 and SA.sub.14, which have the perpendicularity error W, a uniform overlay error .DELTA.x arises in the direction X between the pattern in the shot area SB.sub.1 and the pattern in each of the shot areas SA.sub.11 to SA.sub.14 of the preceding layer. Assuming that the length of each side of the shot area SA.sub.11 is L, the overlay error .DELTA.x is approximately L.multidot.W/2.
In a case where each shot area of the preceding layer has a shot rotation (chip rotation) also, an overlay error arises which is similar to that in a case where the angle between the X- and Y-axes of the shot array deviates from 90.degree..
FIG. 36 shows the four shot areas SA.sub.11 to SA.sub.14 in a situation where the perpendicularity error of the shot array is zero, but the shot rotation is .theta. [rad]. Let us assume that the shot rotation .theta. is of the same size as the perpendicularity error W in FIG. 35. In the case of FIG. 36, even if the subsequent shot area SB.sub.1 is exposed by rotating it simply through an angle corresponding to the shot rotation .theta., a uniform overlay error .DELTA.x of the same size as that in the case of FIG. 35 arises in the direction of the shot rotation between the pattern in the shot area SB.sub.1 and the pattern in each of the shot areas SA.sub.11 to SA.sub.14 of the preceding layer.
That is, when exposure is sequentially carried out by using exposure apparatuses having respective exposure fields of different sizes, if the array of shot areas of the preceding layer has a perpendicularity error or a shot rotation, a uniform overlay error arises if the subsequent shot areas are simply aligned with respect to the preceding shot areas.
On the other hand, in the above-described mix-and-match method, in which after a layer on a wafer has been exposed by a first exposure apparatus, overlay exposure is carried out on the preceding layer by using a second exposure apparatus, the second exposure apparatus may effect alignment by an enhanced global alignment (hereinafter referred to as "EGA") method as disclosed, for example, in Japanese Patent Application Unexamined Publication (KOKAI) (hereinafter referred to as "JP(A)") No. 61-44429 (corresponding to U.S. Pat. No. 4,780,617). In this case, however, some problems are experienced, which will be explained below with reference to FIGS. 37(a) to 38(c).
FIGS. 37(a), 37(b) and 37(c) illustrate a related art in which exposure is carried out by the mix-and-match method using two exposure apparatuses having respective exposure fields of the same size. First, a pattern image of a reticle RA shown in FIG. 37(b) is transferred onto each of shot areas 129A, 129B, . . . , 129I of a first layer, which are shown by the chain lines in FIG. 37(a), on a wafer 20 by using a first exposure apparatus. In this case, it is assumed that a coordinate system that defines each particular travel position of a wafer stage of the first exposure apparatus (i.e. stage coordinate system) comprises an X1-axis and a Y1-axis, and that the Y1-axis is tilted by an angle W clockwise from an ideal Y1*-axis which is perpendicular to the X1-axis. Further, the reticle RA has two identical circuit patterns 112A and 112B (i.e. two-chip pattern) formed in a pattern area 42A. The rotation angle of the reticle RA has been set so that the circuit patterns 112A and 112B are arrayed in a direction perpendicular to the X1-axis when exposure is carried out.
As a result, the shot areas 129A to 129I of the first layer are arrayed at a predetermined pitch along each of the X1- and Y1-axes, and the shot array has a perpendicularity error W. Further, two identical circuit pattern images are transferred onto each of the shot areas 129A to 129I in such a manner as to lie in side-by-side relation to each other in a direction perpendicular to the X1-axis.
Next, a pattern image of a reticle RC shown in FIG. 37(c) is transferred onto each of shot areas of a second layer on the wafer 20 by using a second exposure apparatus. In this case, it is assumed that a stage coordinate system of the second exposure apparatus comprises an X2-axis and a Y2-axis, and that a direction corresponding to the X1-axis of the first layer on the wafer 20 has been set parallel to the X2-axis by pre-alignment carried out in the second exposure apparatus. Although the origins of the coordinate systems (X1,Y1) and (X2,Y2) in FIG. 37(a) have been set at the center of the wafer 20 for the sake of explanation, it should be noted that the origins of these coordinate systems may be set at any positions. The reticle RC also has two identical circuit patterns 127A and 127B formed in a pattern area 42C, and the image of the pattern area 42A of the reticle RA as projected on the wafer 20 (i.e. exposure field) and the projected image (exposure field) of the pattern area 42C of the reticle RC are of the same size.
In this case, the second exposure apparatus effects alignment by the above-described EGA method. That is, array coordinates of wafer marks (not shown) provided for a predetermined number of shot areas (sample shots) selected from the first layer on the wafer 20 are measured to thereby calculate array coordinates of all the shot areas in the stage coordinate system (X2,Y2). Thus, the second exposure apparatus can recognize that the perpendicularity error W is present in the shot array on the first layer.
In the second exposure apparatus, therefore, the rotation angle of the reticle RC is set so that the two circuit patterns 127A and 127B are arrayed in a direction perpendicular to the X2-axis, as shown in FIG. 37(c), and thereafter, a shot array of a second layer is set by taking into consideration the perpendicularity error W. Then, exposure is carried out. As a result, the circuit pattern images of the reticle RC are transferred onto each of shot areas 130A, 130B, . . . , 130I of the second layer, shown by the solid lines in FIG. 37(a), on the wafer 20. Thus, the shot array of the second layer is accurately overlaid on the shot array of the first layer.
In a case where the exposure fields (shot areas) of two exposure apparatuses have the same size as described above, even if the shot array of the first layer has a perpendicularity error, the overlay accuracy between the first and second layers can be maintained at high level by effecting alignment according to the EGA method, for example.
However, if the shot array of the first layer has a perpendicularity error in a case where the exposure fields of the two exposure apparatuses have different sizes, the overlay accuracy between the two layers cannot be increased above a certain level by an ordinary exposure method.
FIGS. 38(a), 38(b) and 38(c) illustrate a related art in which exposure is carried out by the mix-and-match method using two exposure apparatuses having respective exposure fields of different sizes. First, a pattern image of a two-chip reticle RA, which has two identical patterns 112A and 112B written in a pattern area 42A as shown in FIG. 38(b), is transferred onto each of shot areas of a first layer on a wafer 20 by using a first exposure apparatus. Next, a pattern image of a three-chip reticle RB, which has three identical circuit patterns 113A to 113C written in a pattern area 42b as shown in FIG. 38(c), is transferred onto each of shot areas of a second layer on the wafer 20 by a second exposure apparatus. The image of the reticle RB as projected on the wafer 20 has the same horizontal width as that of the projected image of the reticle RA, but the vertical width of the projected image of the reticle RB is 3/2 times that of the reticle RA.
In this case also, the stage coordinate system of the first exposure apparatus is denoted by (X1,Y1), and the stage coordinate system of the second exposure apparatus is denoted by (X2,Y2), and it is assumed that alignment and exposure are carried out with the X2-axis aligned with the X1-axis. When exposure is carried out with the first exposure apparatus by setting the reticle RA so that the two circuit patterns of the reticle RA are arrayed in a direction perpendicular to the X1-axis, the circuit patterns are transferred onto each of shot areas 129A, 129B, 129I of the first layer, shown by the chain lines in FIG. 38(a), on the wafer 20. In this case also, the array of the shot areas 129A to 129I has a perpendicularity error in the same way as in the example shown in FIGS. 37(a) to 37(c).
Thereafter, the wafer 20 is aligned by the EGA method using a second exposure apparatus, and then exposure is carried out in such a manner that the three circuit patterns of the reticle RB are arrayed in a direction perpendicular to the X2-axis. Consequently, the three circuit patterns are transferred onto each of shot areas 131A to 131F of the second layer on the wafer 20, as shown by the solid lines in FIG. 38(a). However, because each shot area of the first layer has two circuit patterns transferred thereto, while each shot area of the second layer has three circuit patterns transferred thereto, the shot array of the first layer and the shot array of the second layer undesirably differ from each other in the number of rows in a direction approximately perpendicular to the X1-axis. As a result, it becomes impossible to eliminate the effect of a perpendicularity error, which is an error between the rows or columns of a shot array. For example, in FIG. 38(a), if the shot area 129A and the shot area 131A are aligned in the direction X1 (or X2), a large overlay error arises in the direction X1 between the shot area 129B and the shot area 131A.
Meanwhile, if both a first and second exposure apparatuses employ the EGA method, the following problems arise. The problems will be explained below with reference to FIGS. 39(a) to 41(b).
In this EGA process, array coordinates of a predetermined number of shot areas (sample shots), which have previously been selected from among shot areas on a wafer, are measured to determine, for example, six coordinate transformation parameters for calculating array coordinates in a stage coordinate system, in which the wafer stage is to be positioned, from the design array coordinates of all the shot areas.
However, when a pattern for a middle layer is transferred onto a critical layer by the mix-and-match exposure method, for example, a given overlay error may remain if the coordinate transformation parameters obtained by the EGA method (hereinafter occasionally referred to as "EGA parameters") are used as they are because different projection exposure apparatuses are used for the critical and middle layers. This means that the EGA parameters may have residual errors. In order to correct such residual errors, the conventional practice is to measure overlay errors by conducting test printing using marks or overlay accuracy measurement (hereinafter referred to as "vernier marks"), as described below.
FIG. 39(a) shows a wafer 20 having vernier marks formed by a projection exposure apparatus for exposure of a critical layer. In FIG. 39(a), shot areas SE1, SE2, . . . , SEM (M is an integer of 12 or more, for example) are arrayed on the wafer 20 at a predetermined pitch along each of the X- and Y-axes of an orthogonal coordinate system (X,Y). In each shot area SEm (m=1 to M), alignment marks (wafer marks) and overlay accuracy measuring vernier marks have been formed.
FIG. 39(b) is an enlarged view showing the mark arrangement in a shot area SEm. In FIG. 39(b), the shot area SEm has a wafer mark 221X for the X-axis formed at an end in the direction +Y. The wafer mark 221X comprises line-and-space patterns arranged at a predetermined pitch in the direction X. The shot area SEm further has a wafer mark 221Y for the Y-axis formed at an end in the direction +X. The wafer mark 221Y comprises line-and-space patterns arranged at a predetermined pitch in the direction Y. The wafer marks 221X and 221Y are marks which are detected by an imaging detection method (FIA method). Further, the shot area SEm has vernier marks 222A to 222E formed therein at respective positions which are distributed in a cross shape. The vernier marks 222A to 222E are, for example, box-in-box marks which are detected by an imaging detection method (image processing detection method).
Next, predetermined vernier marks are overlaid on the wafer 20 shown in FIG. 39(a) by exposure using a projection exposure apparatus for a middle layer. For the overlay exposure, it is necessary to obtain array coordinates of each shot area SEm (m=1 to M) on the wafer 20 in the stage coordinate system of the projection exposure apparatus for a middle layer. Therefore, it is assumed that the wafer marks 221A and 221Y of each shot area SEm (m=1 to M) indicate the coordinates of the center of the corresponding shot area. It is further assumed that the design array coordinates of the center of each shot area SEm (m=1 to M) in the coordinate system on the wafer 20 (i.e. the sample coordinate system) are (Dxn,Dyn), and that the computational array coordinates of each shot area SEm (m=1 to M) in the stage coordinate system of the projection exposure apparatus for a middle layer are (Fxn,Fyn). In this case, the X component Dxn and Y component Dyn of the design array coordinates of the center of each shot area SEm are the X coordinate of the corresponding wafer mark 221X and the Y coordinate of the corresponding wafer mark 221Y, respectively, which may be approximately expressed by the following equation (1): ##EQU1##
The transformation matrix in Eq. (1) has as elements six coordinate transformation parameters (EGA parameters), including scaling parameters Rx and Ry, rotation .THETA., perpendicularity W, and offsets Ox and Oy. The scaling parameters Rx and Ry are linear expansion and contraction quantities in the directions X and Y, respectively. The rotation .THETA. is an angle of rotation of the wafer 20. The perpendicularity W is a perpendicularity error, that is, a deviation of the intersection angle between the X- and Y-axes from 90.degree.. The offsets Ox and Oy are shift quantities in the directions X and Y, respectively. Next, in order to determine values of the six coordinate transformation parameters, the projection exposure apparatus for a middle layer measures array coordinates in the stage coordinate system of the wafer marks 221X and 221Y provided for each of, for example, 10 shot areas (sample shots) SEa, SEb, SEc, . . . , SEj selected from among the shot areas on the wafer 20 shown in FIG. 39(a). The sample shots SEa to SEj are disposed at the vertices of an approximately regular polygon on the surface of the wafer 20 or at uniformly dispersed random positions.
In this case, the measured values of the array coordinates in the stage coordinate system of the wafer marks 221X and 221Y obtained by the n-th measuring operation (n=1 to 10), that is, the measured array coordinates of the center of the n-th sample shot, are assumed to be (Mxn,Myn). Next, the design array coordinates (Dxy,Dyn) of the wafer marks 221X and 221Y are substituted into the right-hand side of Eq. (1) to obtain computational array coordinate values (Fxn,Fyn). Then, deviations of the measured coordinate values (Mxn,Myn) from the computational array coordinate values (Fxn,Fyn), that is, alignment errors (Exn,Eyn)(=(Mxn-Fxn,Myn-Fyn)), are obtained. Thereafter, values of the six EGA parameters are determined so as to minimize the sum of the squares of the alignment errors obtained for all the sample shots, that is, the residual error component.
Assuming that the number of measured sample shots is K (K=10 in FIG. 39(a)), the residual error component is expressed by the following equation (2). For example, values of the six EGA parameters (scaling parameters Rx, Ry, wafer rotation .THETA., perpendicularity W, and offset quantities Ox, Oy) are obtained by solving simultaneous equations established by setting the result of partial differentiation of Eq. 2 with respect to each of the six EGA parameters equal to zero. ##EQU2##
Next, the six EGA parameter values thus obtained and the design array coordinate values (Dxm,Dym) of each shot area SEm (m=1 to M) are sequentially substituted into the right-hand side of Eq. (1), thereby obtaining array coordinate values in the stage coordinate system of each shot area SEm of the critical layer on the wafer 20. Assuming that the demagnification ratio for the critical layer is 5:1, while the demagnification ratio for the middle layer is 2.5:1, that is, the exposure field of the projection exposure apparatus for the middle layer is 2 times as large as the exposure field of the projection exposure apparatus for the critical layer in both the directions X and Y, each middle layer shot area contains four critical layer shot areas.
Therefore, when exposure is to be carried out by the middle layer projection exposure apparatus, the critical layer shot areas SEm (m=1 to M) shown in FIG. 39(a) are divided into a plurality of blocks each comprising two shot areas in the direction X and two shot areas in the direction Y, and array coordinates in the stage coordinate system of the center of each block are obtained from the computational array coordinates of the four shot areas in the block. Thereafter, the array coordinates of the center of each block on the wafer 20 are sequentially aligned with the center of the exposure field of the middle layer projection exposure apparatus, and a pattern image of a reticle for the middle layer, which contains vernier marks, is transferred onto each block by exposure. After the exposure process, the wafer 20 is subjected to development process.
FIG. 40(a) shows the wafer 20 having overlaid vernier marks formed by the middle layer projection exposure apparatus. In FIG. 40(a), shot areas SF1, SF2, . . . , SFN (N is an integer of 3 or more, for example) of the middle layer are arrayed on the wafer 20 at a predetermined pitch along each of the X- and Y-axes, and each shot area SFn (n=1 to N) contains four critical layer shot areas. Further, the center 261 of each shot area SFn is approximately coincident with the center of the corresponding block of four critical layer shot areas. Each shot area SFn has 20 (=4.times.5) vernier marks corresponding to a total of 20 vernier marks of the critical layer, that is, four groups of five vernier marks 222A to 222E (see FIG. 40(b)).
Here, four shot areas SFa to SFd (shaded shot areas in FIG. 40(a)) are defined as objects to be measured, and amounts of positional displacement of the middle layer vernier marks relative to the critical layer vernier marks are measured, for example, at measuring points 262 to 265 selected at random in the shot areas SFa to SFd. FIG. 40(b) shows the shot area SFa among the four. In FIG. 40(b), the middle layer shot area SFa has middle layer vernier marks 224A to 224E, 226A to 226E, 228A to 228E, and 230A to 230E formed to surround the vernier marks, respectively, which belong to four critical layer shot areas SEp, SE(p+1), SEq and SE(q+1), which underlie the shot area SFa. Accordingly, at the measuring point 262 in the shot area SFa, an amount of positional displacement in the direction X or Y of the middle layer vernier mark 226C relative to the critical layer vernier mark 222C in the shot area SE(p+1) is measured. Similarly, an amount of positional displacement between the two corresponding vernier marks is measured at each of the measuring points 263 to 265.
Consequently, if all the critical layer vernier marks are displaced, for example, by a predetermined amount .delta.X in the direction X relative to the middle layer vernier marks at all the measuring points 262 to 265, in FIG. 40(a), it is revealed that the X-axis offset Ox in the EGA parameters has a residual error .delta.X. Therefore, the residual error is previously stored in a control system of the middle layer projection exposure apparatus as a system constant to correct an alignment result, thereby making it possible to form a middle layer pattern over the critical layer by exposure with high overlay accuracy.
Thus, residual errors of the EGA parameters can be corrected by measuring amounts of positional displacement between the critical layer vernier marks and the middle layer vernier marks. However, no particular consideration has heretofore been given to the arrangement of measuring points for measuring amounts of positional displacement between the critical layer vernier marks and the middle layer vernier marks, as shown by the measuring points 262 to 265 in FIG. 40(a). Accordingly, when the projected image for the middle layer has a magnification error or a rotation error, for example, the magnification or rotation error may be erroneously judged to be a residual error of the EGA parameters.
The above problem will be explained below with reference to FIGS. 40(a) to 41(b). FIG. 41(a) shows a state where the middle layer shot area SFa is slightly enlarged relative to a projected image 266 obtained when there is no magnification error. As shown in FIG. 41(a), in the central portion at the right end of the first quadrant of the shot area SFa (i.e. the critical layer shot area SE(p+1)), the middle layer vernier mark 226C is displaced relative to the critical layer vernier mark 222C by .DELTA.x1 and .DELTA.y1 in the directions X and Y, respectively. In the center portion at the right end of the second quadrant (i.e. the shot area SEp), the middle layer vernier mark 224C is displaced relative to the critical layer vernier mark 222C by approximately .DELTA.y1 in the direction Y, but the amount of displacement in the direction X of the middle layer vernier mark 224C is so small as to be ignorable. Similarly, in the third quadrant (i.e. the shot area SEq) and the fourth quadrant (i.e. the shot area SE(q+1)), the two vernier marks are displaced in symmetric relation to those in the second and first quadrants, respectively.
When a projected image of the middle layer has such a magnification error, if an amount of positional displacement in the direction X between the two corresponding vernier marks is measured at the measuring point 265 in the first quadrant of the shot area SFd, shown in FIG. 40(a), and at the measuring point 263 in the second quadrant of the shot area SFb, shown in FIG. 40(a), the results of the measurement are .DELTA.x1 and 0, respectively. Accordingly, if residual errors of the EGA parameters of Eq. (1) are obtained by simply processing these amounts of positional displacement, predetermined errors remain in the scaling parameter Rx and offset Ox in the direction X, respectively.
If an amount of positional displacement in the direction X between the two corresponding vernier marks is measured at the measuring point 262 in the first quadrant of the shot area SFa, shown in FIG. 40(a), and at the measuring point 264 in the second quadrant of the shot area SFc, shown in FIG. 40(a), the results of the measurement are .DELTA.x1 and 0, respectively. Accordingly, if residual errors of the EGA parameters of Eq. (1) are obtained by simply processing these amounts of positional displacement, predetermined errors remain in the perpendicularity W and the offset Ox in the direction X, respectively. That is, if an amount of positional displacement in the direction X between two corresponding vernier marks is measured at measuring points in middle layer shot areas defined as objects to be measured, which measuring points are in different columns on the critical layer, the magnification error of the middle layer may be mistaken for a residual error (linear error) in the EGA parameters. Such erroneous recognition may also occur in the case of measuring an amount of positional displacement in the direction Y between two corresponding vernier marks.
FIG. 41(b) shows a state where the middle layer shot area SFa has been rotated counterclockwise relative to the projected image 266 obtained when there is no error (i.e. a state where the shot area SFa has a shot rotation error). As shown in FIG. 41(b), in the central portion at the right end of the first quadrant of the shot area SFa, the middle layer vernier mark 226C is displaced relative to the critical layer vernier mark 222C by -.DELTA.x2 and .DELTA.y2 in the directions X and Y, respectively. In the central portion at the right end of the second quadrant (i.e. the shot area SEp), the middle layer vernier mark 224C is displaced relative to the critical layer vernier mark 222C by approximately -.DELTA.x3 in the direction X, but the amount of displacement in the direction Y of the middle layer vernier mark 224C is so small as to be ignorable. Similarly, in the third and fourth quadrants, the two corresponding vernier marks are displaced in symmetric relation to those in the second and first quadrants, respectively.
When a projected image of the middle layer has such a rotation error, if an amount of positional displacement in the direction X between two corresponding vernier marks is measured at the measuring point 265 in the first quadrant of the shot area SFd, shown in FIG. 40(a), and at the measuring point 263 in the second quadrant of the shot area SFb, shown in FIG. 40(a), the results of the measurement are -.DELTA.x2 and -.DELTA.x3, respectively. Accordingly, if residual errors in the EGA parameters of Eq. (1) are obtained by simply processing these amounts of positional displacement, an error remains in a parameter other than the offset Ox among the EGA parameters of Eq. (1). When an amount of positional displacement in the direction Y between two corresponding vernier marks is measured at each of the measuring points 265 and 263, an error similarly remains in an EGA parameter other than the offset Oy. Thus, it will be understood that, when amounts of positional displacement between the critical layer vernier marks and the middle layer vernier marks are measured to correct residual errors of the EGA parameters, a mere magnification error or rotation error of a middle layer shot area may be mistaken for a residual error of an EGA parameter other than the offsets Ox and Oy depending upon the selection of the positions of measuring points in middle layer shot areas as objects to be measured.
When critical layer shot areas (chip patterns) have a magnification error or a rotation error (chip rotation), such an error may also be mistaken for a residual error of an EGA parameter other than the offsets Ox and Oy depending upon the selection of measuring points for measuring amounts of positional displacement between the corresponding vernier marks.
As has been described above, residual errors of the EGA parameters can be corrected by measuring amounts of positional displacement between the critical layer vernier marks and the middle layer vernier marks. However, there may be residual errors not only in the above-described coordinate transformation parameters related to the whole wafer but also in so-called in-shot parameters comprising shot magnifications (i.e. linear expansion and contraction of each chip pattern in the directions X and Y) rx and ry, shot rotation (i.e. a rotation angle of each chip pattern) .theta., and shot perpendicularity (i.e. a perpendicularity error of the coordinate system in each chip pattern) w.
To obtain a correction value for the shot magnification rx, for example, it is conceivable to measure an amount of positional displacement between two corresponding vernier marks at each of the two opposite measuring points 262 and 266 in the shot area SFa shown in FIG. 40(a). A residual shot magnification error, i.e. a correction value for the shot magnification rx, should be calculable from the difference between the X components of the amounts of positional displacement measured at the two measuring points 262 and 266. Similarly, a residual shot rotation error should be calculable.
In actual practice, however, the vernier mark positions on the critical layer may have different stepping errors because the measuring points 262 and 266 belong to different shot areas SE(p+1) and SEp on the critical layer. That is, if no consideration is given to the arrangement of measuring points at which vernier marks are to be read, variation due to the stepping accuracy of the wafer stage may be mistaken for a residual shot magnification error or a residual shot rotation error. If an erroneous correction value is used to correct the corresponding in-shot parameter, the alignment accuracy reduces disadvantageously.